Abstract: Nonuniform fast Fourier transformation(NUFFT),as an efficient method for irregular sampling problem,is widely used in signal processing.This article gives a review of the history and development of NUFFT,followed by a detailed depiction of the general scheme of the algorithm.The newly improvements in the past few years is also discussed.Finally,it is shown that NUFFT performs well in CT reconstruction,such as Fourier reconstruction,iterative reconstruction and sparse sampling problems.